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WASHINGTON — A $1.2 trillion omnibus bill to fund the government is headed for a Senate vote that will put lawmakers on the spot over the practice of earmarking money for such projects as the Edward M. Kennedy Institute of the US Senate in Boston, which would receive $8 million in the measure.

The 1,924-page bill, unveiled by Democrats yesterday, includes thousands of such earmarks and comes about a month after Republicans adopted a nonbinding moratorium on pushing for such projects. The Senate’s Democratic majority aims to overcome that objection with the help of Republicans such as Senators George Voinovich of Ohio and Bob Bennett of Utah who scoff at complaints over the projects.

“I have a disagreement with my colleagues on earmarks’’ Voinovich told reporters. “We’re fooling the American people when we tell them the problem is earmarks.’’

Senator Jim DeMint, a South Carolina Republican, urged his colleagues to deny Democrats the votes needed to advance the bill that finances government agencies and programs for the fiscal year that ends Sept. 30, 2011.

“All of us know that it’s really bad for our party to pass an omnibus with earmarks,’’ he said.

Democrats, who control the Senate with 58 votes, would need 60 votes to overcome procedural hurdles. Senate Appropriations Committee Chairman Daniel Inouye, a Hawaii Democrat, said he is confident the measure would be passed before Congress adjourns for the year.

The bill’s earmarks would cost about $8 billion, said Rob Blumenthal, an Inouye spokesman.

Senator John F. Kerry submitted the provision for $8 million that would go toward the Kennedy Senate center, being built next to the John F. Kennedy Presidential Library and Museum in Dorchester.

The institute, also being funded through private donations, has already received $38.3 million in funds through earmarks.

The bill also includes $450 million for a program that is developing a second engine for the F-35 Joint Strike Fighter, despite objections from the Pentagon and a veto threat from the Obama administration. That funding, considered wasteful by the Obama White House, is supported by most of the Massachusetts congressional delegation because it would help preserve jobs at a General Electric plant in Lynn.

And it includes funding for the Navy to double an order of coastal combat ships — from 10 ships to 20 — that would expand the program and would bring 500 new jobs to a General Dynamics computer manufacturing plant in Pittsfield.

A stopgap measure funding the government expires Dec. 18. If Senate Democrats fall short of the 60 votes needed to proceed on their bill, they will likely take up a House-passed version of the measure that omits earmarks. Republicans in both chambers have been pushing for a short-term funding extension into early next year.

The legislation unveiled yesterday includes about $20 billion more than the House plan, according to a summary provided by the Senate Appropriations Committee. Like the House bill, it includes provisions opposed by the White House that would bar the administration from bringing Khalid Sheikh Mohammed or other terrorist suspects held at Guantanamo Bay, Cuba, to the United States for trial.